Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-7x+5y &= -8 \\ 7x+3y &= -9\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $7x = -3y-9$ Divide both sides by $7$ to isolate $x$ $x = {-\dfrac{3}{7}y - \dfrac{9}{7}}$ Substitute this expression for $x$ in the first equation. $-7({-\dfrac{3}{7}y - \dfrac{9}{7}}) + 5y = -8$ $3y + 9 + 5y = -8$ Simplify by combining terms, then solve for $y$ $8y + 9 = -8$ $8y = -17$ $y = -\dfrac{17}{8}$ Substitute $-\dfrac{17}{8}$ for $y$ in the top equation. $-7x+5( -\dfrac{17}{8}) = -8$ $-7x-\dfrac{85}{8} = -8$ $-7x = \dfrac{21}{8}$ $x = -\dfrac{3}{8}$ The solution is $\enspace x = -\dfrac{3}{8}, \enspace y = -\dfrac{17}{8}$.